TSP is actually less caustic than the main ingredient in dishwasher detergent, which is washing soda or sodium carbonate.
And yes, STPP would be preferable to TSP, since STPP doesn't create an insoluble precipitate to encrust glassware, dishware, and dishwasher parts.
To date I'm still using phosphated DW detergents. I bought up a stash before the products disappeared from the shelves. At some point I'll try Finish or the new Cascade to see if these new formulations have finally come up to performance level of the older phosphated formulations.
It's also unfortunate - for those of us with vintage dishwashers with relatively quick wash cycles - that chlorinated DW detergent is no longer available. I doubt that the enzymes in modern DW detergents have enough time to work in, say, the 10 minute wash portion of KD2P dishwasher cycle.